Is This Move Rational?

In college basketball, when a star player gets his fourth foul, coaches usually sit him for a long time, to save him for the end of the game. I've often wondered if this makes any sense. Here is my case for doubting that it does:

1) You don't know how long it will be before foul five, so you run a high risk of benching a player for too long. For instance, perhaps he would have gone ten minutes before getting foul five, but the coach holds him out until only five minutes are left in the game: five minutes were "wasted" playing without the fellow.

2) The usual response to this would be, I think, "But we need to make sure he is on the floor at the end of the game"

Why? Baskets in the first minute of a game count for exactly the same number of points as those in the last minute. Let's say the star who was held out brings his team from ten down to win by one in the last five minutes. The coach will claim vindication: "See, he saved the game for us at the end!"

But, if the star did that, why shouldn't we think that, if he had been in the game earlier, his time would have built up a twelve-point lead, which would be reduced to one after the star got his fifth foul?

I suspect there is an irrational illusion at work here: Because it is the score when the buzzer sounds that matters, somehow the last few minutes seem more important than any others.

2 comments:

As a former baller and ocassional youth coach, I believe it is absolutely rational to manage players with 4 fouls for strategic reasons. The problem is that managing players with 4 fouls has become such an ingrained part of game planning for most coaches that they do it even when there is no strategic advantage for doing so. Theoretically managing fouls when it's not necessary could backfire, but I personally have never seen it happen; at most it was just a meaningless gesture.

Assuming a highly competitive game, my counterargument to you would be this: getting the 4th foul too early incentivizes the star player to play to not foul out, which will tend to hinder the team's production.

If the star player is a defensive specialist, for example, the early 4th foul will tend to make him play softer defense, which forces the rest of the team to make up for it somehow. In this situation, the value of the star player staying on the court will tend to drop below the value of his best bench replacement with ample fouls to give. If the rest of the team can compensate for the bench player similarly to how they would've for the star player anyway (and often times the team will compensate better for the bench player because he's in), it's a worthwhile risk to put the bench player in.

The potential reward is even greater if the foul situation changes in such a way that, at a critical juncture, the value of the other team's next foul negates the value of your star player's next foul when he re-enters the game.

I guess to summarize with respect to your argument: while the value of a basket is constant throughout the course of a game, the value of a player is not; certain factors may render him highly effective at some points in the game and less effective at others. The trick is maximizing your best players (or your best possible lineup) when they can be the most effective.